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<strong>Pharmacokinetics</strong>Analysis of experimental data...In real pharmacokinetic experiments, it is generally unrealistic to try to obtain a blood sample at time zero, as this wouldmean injecting the drug into one vein and taking a sample out of another simultaneously. The normal solution is to fit aline or curve to the data and back-extrapolate to time zero to determine what the initial concentration must have been,although no sample was actually taken at that time. This is referred to as the ‘Theoretical C 0’.It is obvious from Figure 6.1 that there would be a great deal of subjectivity in fitting a curve to the points and, in particular,the attempted extrapolation of the curve is highly error prone. Several analysts attempting to fit and extrapolate a curvewould probably produce a wide range of estimates for theoretical C 0.6.1.2 Linearizing the data using semi-log graph paperIt would be much more satisfactory if we could modify the plotting procedure so that the points formed a straight line(linearization). The first appendix to this chapter demonstrates that plotting the data onto semi-log graph paper willachieve linearization. This paper has a logarithmic vertical scale which means that we are effectively plotting the log ofthe concentration versus time instead of the simple concentration versus time.Excellent quality, semi-log graph paper can be downloaded (free) from www.customgraph.com. From Linear / Semi-Log/ Log-Log etc, select Semi-Log. Set Orientation: to Portrait and set Log Cycles: to the appropriate number (2 for thepresent case).The plotted graph is shown in Figure 6.2. There are a number of things to note concerning semi-log graphs.--The vertical scale is ‘Logarithmic’ – it has uneven spacing which means that when the drug concentrationsare plotted onto this scale, the graph is linearized.--The horizontal scale is a simple linear scale. Because only one axis is logarithmic, the paper is referred to as‘Semi-log’.--The vertical scale covers two orders of magnitude, allowing us to plot a maximum of a 100-fold range ofdrug concentrations. In this case the vertical scale has been numbered from 0.1 to 1.0 (1 st cycle) and thenfrom 1 to 10 (2 nd cycle). If the observed drug concentrations had been higher or lower, then the axis couldhave been numbered from (say) 1 to 100 or from 0.01 to 1.0. In all these cases, there is a 100-fold range ofvalues. If the observed drug concentrations had covered a wider range, then semi-log paper with more cycleswould be required. Three-cycle paper will allow for a 1,000-fold range of concentrations and four-cycle,10,000 and so on. For our purposes, two-cycle paper is adequate.--The numbering of the vertical axis must begin at some exact power of 10. Thus it is acceptable to start at0.001, 0.01, 0.1, 1, 10, 100, 1,000 etc. However, it cannot begin at (say) 2 or 3.5 and in particular, it cannotbegin at zero. For our purposes, the lowest concentration to be accommodated is 0.19mg/L and so thenumbering has started at 0.1.--We need to be able to back-extrapolate the graph to obtain the theoretical initial concentration (C 0) and sonumbering of the horizontal axis must begin at time zero, even though the first sample was not taken until twohours.Notice that we only obtain a straight line from a semi-log plot if the drug occupies one compartment. When data for adrug that occupies two compartments is plotted on semi-log paper the graph has a clear bend in it.58Download free ebooks at bookboon.com
<strong>Pharmacokinetics</strong>Analysis of experimental data...It is common to see pharmacokinetic data plotted as the log of the concentration versus time or (more likely)presented on a semi-log graph.We now need to read off two values from Figure 6.2:--The theoretical C 0--The drug half-life Figure 6.2 Concentration versus time on semi-log graph paper59Download free ebooks at bookboon.com
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